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A108019 a(n) = (8^n - 1)*4/7.

%I A108019 #28 Apr 20 2020 14:48:01
%S A108019 0,4,36,292,2340,18724,149796,1198372,9586980,76695844,613566756,
%T A108019 4908534052,39268272420,314146179364,2513169434916,20105355479332,
%U A108019 160842843834660,1286742750677284,10293942005418276,82351536043346212
%N A108019 a(n) = (8^n - 1)*4/7.
%C A108019 Numbers n whose binary representation is 100, n times.
%H A108019 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,-8).
%F A108019 a(n) = 8*a(n-1) + 4 with n>0, a(0)=0. - _Vincenzo Librandi_, Nov 13 2010
%F A108019 From _Colin Barker_, Oct 15 2012: (Start)
%F A108019 a(n) = 9*a(n-1) - 8*a(n-2).
%F A108019 G.f.: 4*x/((x-1)*(8*x-1)). (End)
%e A108019 a(3)=292 because 292 translated in base 2 is three times 100: 100100100.
%e A108019 From _Zerinvary Lajos_, Jan 14 2007: (Start)
%e A108019 Octal............Decimal
%e A108019 0......................0
%e A108019 4......................4
%e A108019 44....................36
%e A108019 444..................292
%e A108019 4444................2340
%e A108019 44444..............18724
%e A108019 444444............149796
%e A108019 4444444..........1198372
%e A108019 44444444.........9586980
%e A108019 444444444.......76695844
%e A108019 4444444444.....613566756,
%e A108019 etc. (End)
%t A108019 Table[ FromDigits[ Flatten[ Table[{1, 0, 0}, {i, n}]], 2], {n, 0, 19}] (* _Robert G. Wilson v_, Jun 01 2005 *)
%t A108019 s=0;lst={s};Do[s+=2^n;AppendTo[lst, s], {n, 2, 5!, 3}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 07 2008 *)
%t A108019 NestList[8#+4&,0,20] (* _Harvey P. Dale_, Aug 08 2013 *)
%o A108019 (PARI) a(n)=if(n<0, 0,(8^n-1)*4/7) /* _Michael Somos_ */
%Y A108019 Cf. A020988.
%K A108019 nonn,easy
%O A108019 0,2
%A A108019 _Alexandre Wajnberg_, May 31 2005
%E A108019 More terms from _Robert G. Wilson v_, Jun 01 2005